**Abstract **Physicist, and founder of the Shroud of Turin Research Project (STURP), John P. Jackson. has proposed that the image features of the Shroud of Turin were produced by radiation emanating from the body in the Shroud at the moment of resurrection. To many, the concept of resurrection is patently absurd, but it is argued here that any apparent absurdity is the result of a conflict between this concept and a false world-view in terms of which resurrection contravenes physical laws. Jackson has proposed also that “the Shroud image presents, if you will, some type of “new physics” that ultimately requires an extension or even revision of current concepts,” and the purpose of this note is to show that, if certain deep-rooted but inadequate concepts are extended and revised, we will be able to explain the resurrection, and the image on the Shroud, in a way that coheres with both with the biblical account of the life of Yeshua ben Yosef (a.k.a. Jesus of Nazareth) and with science.

PART I: INTRODUCTION TO THE SHROUD

**Background**

The Shroud of Turin is a 14.3 foot by 3.7 linen cloth bearing the faint double-image (ventral and dorsal) of a naked man who appears to have been crucified (together with burn marks and water stains resulting from fires, one in 1532). It is supposed by millions of Christians to be the burial Shroud of Jesus of Nazareth, or more correctly Yeshua ben Yosef. There is a puncture wound on his left wrist (his right wrist is hidden from view), and there are puncture wounds on his feet. The back of the man is covered with over 120 scourge marks, apparently imposed by the roman instrument of torture known as the flagrum (a whip with two or three thongs to which were attached small balls of lead). There are wounds on the top of his head, and there is a large puncture wound on the right side between the ribs from which blood and a watery serum have flowed. The image resides only on top-most fibrils of the threads with which the Shroud is woven, and it is a negative image. Although very faint when viewed as a positive, the image becomes much clearer when darks and lights are reversed.

The positioning of the hands over the groin area, the prominence of the chest, the invisibility of the neck, and the foreshortened forehead all indicate that the man in Shroud was, not flat, but was lying with knees and waist bent, and his head bowed.

The Shroud was involved in a fire in 1532, and its most predominant features are scorch marks where molten silver dripped on the cloth, and triangular patches used to mend holes resulting from that fire. In 1978 group of scientists known as STURP (Shroud of Turin Research Project) performed an intensive series of tests on the Shroud. Many were skeptical and expected that they would quickly discover it to be a fake, but after three years of analyzing the data they collected they wrote in their final report:

*We can conclude for now that the Shroud image is that of a real human form of a scourged, crucified man. It is not the product of an artist. The blood stains are composed of hemoglobin and also give a positive test for serum albumin. The image is an ongoing mystery and until further chemical studies are made, perhaps by this group of scientists, or perhaps by some scientists in the future, the problem remains unsolved.*

**The Age of The Shroud**

In 1988, 3 independent laboratories carbon-dated a sample taken from a corner of the Shroud (“Rae’s corner”), and judged the cloth to have been produced with 95% confidence between 1260 and 1390 AD:

This period coincides with the time that the first known expositions of the Shroud are made in the French town of Lirey in 1355. Large crowds of pilgrims converged on Lirey and medallions were struck to mark the occasion. These findings initially limited the popularity of Shroud research, but from the beginning, the question wasn’t so much if the carbon date was right, but why it was *wrong*, for there is considerable forensic and historical evidence that the Shroud predates 1260. First and foremost, the carbon-date implies that the Shroud is a forgery, when all the forensic evidence *other* the the carbon-date implies that it is *not* a forgery: the image on the Shroud was not drawn or painted (there are no binding agents or particulates on the Shroud in the region of the image); it is a negative created at a time when photography didn’t exist, but it is not a photograph (it contains 3d information that photographs do not); and it is not a contact print (parts of the Shroud that were not in contract with the body bear impressions as clear as parts that were in contact with the body); the man on the Shroud has truly been subject to horrific and mortal injuries; he has wounds associated with crucifixion, and the exit wound on his left wrist contradicts the imaginary depictions of the crucifixion in medieval art, but reflects the way in which people were really crucified; he is covered with scourge marks clearly inflicted by the roman instrument of the torture known as the flagrum,

and he has puncture wounds on his head consistent with the wearing of a roughly prepared cap of thorns rather than the imaginary elegant wreath of thorns depicted by medieval artists; there is a large wound on his right side which matches a spear used by roman executioners and from which postmortem blood and a watery serum visible only by ultraviolet fluorescence photography have flowed; the blood on the Shroud is *real* blood and it contains a very high level of bilirubin a substance associated with torture or severe physical trauma; also the Shroud contains traces of pollen from plants growing only in the area of Jerusalem, some of which are extinct since antiquity; there are microscopic traces of dirt at the foot of the man in the Shroud that only match limestone found in the area of Jerusalem… It may even be that there is a faint image of a coin minted by Pontius Pilate between 29 – 32 AD over the right eye of the man in the Shroud. But in any case, the carbon-date contradicts the* history* of the Shroud. First up, there is a Hungarian manuscript dating between 1192 and 1195 -the Pray Codex- that depicts the Shroud with the L-shaped burn marks sustained in an earlier fire:

Deniers maintain that the dots in the Pray codex are decorative, and that the apparent match is purely coincidental, but harder to explain -and suggestive of a much earlier origin for the Shroud than the middle ages- are the ‘Vignon Markings’ named after Paul Vignon, an artist and biologist who studied the Shroud. These are features -including features of the cloth itself rather than the image on the cloth- belonging to the face on the Shroud and to Byzantine portraits of Jesus. The earliest known icon of Christ Pantokrator, for example, was painted in encaustic on panel in the 6th or 7th century and is preserved in Saint Catherine’s monastery deep in the Sinai desert.

The depiction Jesus known as the Pantokrator (meaning ‘ruler of all’) and numerous portraits of Jesus produced after the 6th century exhibit some sub-set of the following:

A deep line in the forehead (1)

A U-shape, between the eyebrows (2)

A downward pointing triangle or V on the bridge of the nose (3)

A second V (4)

A raised left eyebrow (5)

Accentuated left cheek (6)

Accentuated right cheek (7)

An enlarged left nostril (8)

An accent line below the nose (9)

A dark line just below the lower lip (10)

A gap in the beard below the lower lip (11)

A forked beard (12)

A line across throat (13)

Accented owl-like eyes (14)

Two strands of hair (15)

It cannot be sensibly maintained that the Shroud is based on the pantings, rather than the paintings on the Shroud because of the features of the cloth common both to the Shroud and the paintings (such as the line across the throat). And there is the smaller cloth known as the Sudarium of Oviedo, which according to tradition was wrapped around the head of Jesus after he died. Like the Shroud of Turin, the Sudarium of Oviedo is bloodstained, and many stains on the Sudarium match those on the head portion of the Shroud (also the bloodstains on both cloths belong to the same rare and Middle-Eastern type (AB)):

The Sudarium of Oviedo was carbon-dated to 700 AD, but is mentioned in 570 AD as being in a cave near a monastery in Jerusalem… If the Shroud is examined in depth, it quickly becomes difficult to entertain the medieval forgery hypothesis: defenders of this hypothesis are forced by history, science, and by simple common sense, to climb out further and further on a limb that ultimately cannot bear the weight of its improbability.

**part ii: the image on the shroud as a projection**

**The Shroud in 3D**

That there are no pigments or binding agents on the area of the Shroud where the image of the man appears shows that it is not a painting, and the undistorted nature of the dorsal image -in spite of the fact that the bottom part of the cloth must at some point have born the weight of the man’s body- shows that it is not a contact print. Literally speaking, the body-image on the Shroud is the result of the degradation- the aging- of the linen fibers of which the cloth is woven, but question is what caused this degradation. A clue comes from one of the most striking characteristics of the image on the Shroud (and the thing the first prompted the creation of STURP). i.e. the image contains 3D information. This was discovered in 1976 when photograph of the Shroud was fed into a ‘VP8 image analyzer’, a device that is able to convert 2D images into 3D by interpreting darker aspects of the image as being closer, and lighter aspects further away.

Photographs generally don’t contain 3D-information, which arguably leaves us with the sole possibility that the image on the Shroud is an orthographic projection (the representation of a 3 dimensional object on a 2-dimensional surface). Since the image is imprinted only on the underside of the Shroud, it is the result of projection whose light source was the body itself, and since the image does not extend beyond the upper-most fibers of the Shroud, this light source must have possessed a short wave-length. One way in which the image might be construed as a projection involves the the effects of the radiation emanating from the body. *Wikipedia*:

*Since 1930 several researchers (J. Jackson, G. Fanti, T. Trenn, T. Phillips, J.-B. Rinaudo and others) endorsed the flash-like irradiation hypothesis. It was suggested that the relatively high definition of the image details can be obtained through the energy source (specifically, protonic) acting from inside. The Russian researcher Alexander Belyakov proposed an intense, but short flashlight source, which lasted some hundredths of a second. Some other authors suggest the X-radiation or a burst of directional ultraviolet radiation may have played a role in the formation of the Shroud image. From the image characteristics, several researchers have theorized that the radiant source was prevalently vertical. These theories do not include the scientific discussion of a method by which the energy could have been produced.*

In regard to the lack of a method, Jackson in particular suggests that new physics is required to account for it:

*…perhaps the time has come to ask if we ought to start thinking about the Shroud in categories quite different from those that have been considered in the past. In particular, perhaps we need to be more flexible in our scientific approach and consider hypotheses that might not be found readily in conventional modern science, for it is conceivable that the Shroud image presents, if you will, some type of “new physics” that ultimately requires an extension or even revision of current concepts.*

Following on from the research of Benford and Marino, one of the original STURP team, Ray Rogers, showed in 2004 that there are a number of significant differences between the Raes sample and samples taken from the main part of the Shroud in the first scientific examination of the Shroud in 1973. For example, the Raes sample alone contains cotton fibers. Brendan Whiting’s 2006 book, *The Shroud Story*, argued the general case that these differences are due to re-weaving performed on the corner section of the Shroud in the middle ages. This may or may not be a legitimate objection to the veracity of the C-14 date, but in any case is it sufficient to explain an error of over a thousand years? And what about the Sudarium of Oviedo, whose carbon date (700 AD) is 100s of years too young? The figure below -which depicts the high levels of C-14 in the atmosphere during the years in which hundreds of nuclear bombs were being tested- hints at why the radiation/dematerialization hypothesis by itself may offer a better explanation of the incongruously young radio-carbon dates for the Shroud and Sudarium:

Jackson’s view is that the radiation that formed the image accompanied the disintegration of the atoms -the dematerialization- of the body in the Shroud. But if the image on the shroud was produced by the same mechanism as that behind nuclear detonations from 1945, then a great deal of energy would have to be diffused as the body of man in the Shroud dematerialized. This would have wreaked devastation on the surrounding environment. As Manny Carreria objected:

*From the viewpoint of the forces that hold the nucleus together, a very obvious objection can be formulated against any such dematerialization that pulls the particles apart. …the preparation of a 75 kg body requires that about 500 g of mass be changed into pure energy, according to the famous equation of Einstein, E=mc^2 . This same amount of energy will be needed to undo the process and liberate the particles now bound in the heavy nuclei this is the energy of a Megaton nuclear bomb, about 50 x 10^15 joules. Nothing is said about the source of so much energy or about the way to channel it exclusively into the splitting of body atoms, without destroying or drastically affecting all objects in the immediate surroundings.*

A solution to this problem is going to require radically different understanding of the natural world than that provided by the Theory of Relativity and The Standard Model of Particle Physics. To the extent that these theories are right/complete, there is no realistic way to explain how dematerialization could possibly produced the image on the Shroud that makes any sense. Of course, one could simply appeal to a notion of the miraculous that buys you any desired manipulation of nature for free, and give up the quest for scientific sense entirely, but as Jackson says “it is conceivable that the Shroud image presents, if you will, some type of “new physics” that ultimately requires an extension or even revision of current concepts.” As Lee Smolin shows in *The Trouble with Physics*, many of these concepts are flawed -Relativity and Quantum Mechanics contradict each other, and each is beset by absurdities, inadequacies, and unexplained phenomena- and so we need not be afraid to rethink. One of these absurdities concerns the equation E = MC^2 itself, which describes the conversion of mass into energy. A seemingly equivalent form of this equation -E/C^2 = M- describes the reverse conversion of energy into mass, and the question arises as to whether the initial condition of the universe was one of energy or mass. The General Theory of Relativity -which attributes gravity to the curvature of space-time, and the curvature of space-time to mass- implies that this initial condition was one of infinitely compressed matter, i.e. an infinitely massive state. But it is by the Pauli exclusion impossible to compress massive objects into a zero-dimensional location. It is arguable then that energy must be prior to mass, and the initial state of the universe must have be one of infinite energy and zero mass, from which it follows that curvature is due to energy.

A first step toward developing the mathematical foundations of a better theory than Relativity can be taken by considering Euler’s argument in* Variae observations circa series infinitas* (1737). Here he notes that the product continued to infinity of this

in which the numerators are prime numbers and the denominators are one less than the numerators, equals the sum of the infinite series

and they are both infinite. To prove his point to Euler invites us to imagine the extraction from the second series a prime denominator and all remaining multiples of that prime denominator until everything except the first term 1 has been eliminated. Let

Then

This leaves

To eliminate the denominators that are divisible by 3, we divide both sides to get

Subtracting again eliminates all remaining denominators that are multiples of 3 leaving

Applying this eliminatory process to all of the prime numbers leaves

This is a thought-experiment -mere imagination- but if these eliminations could be performed in the physical world, they would result in the disappearance of any distinction between the form and the content of a coordinate system, and therefore the shrinking of space and the slowing of time to a zero-dimensional point. With all of reality contracted to a zero-dimensional point, the distinction between the world and the mind that surveys it is lost. An idea we can take from Euler’s thought-experiment is that, since both prime-density and energy-density must at this point be infinite, this is the state of pure energy required by, but conspicuously missing from the Theory of Relativity. From here we can begin to formulate a theory according to which the development of the universe from this singular point is a process that somehow involves the distribution of the prime numbers.

**The Light-Before-Dark Universe**

*Wolfram Mathworld* defines a projection in this way:

*A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be visualized as shining a (point) light source (located at infinity) through a translucent sheet of paper and making an image of whatever is drawn on it on a second sheet of paper.*

But a “(point) light source” is the same thing as a zero-dimensional light source, which involves the infinite concentration and the zero diffusion of light. The problem with the Wolfram Mathworld definition of projection, and with every physical theory that relies on zero-dimensional point-sources, is that these involve an infinite concentration and zero diffusion of light. Mathematically, this reduces Euler’s number line to the fraction 1/0; physically, it is Einstein’s universe reduced to a state of pure energy. A solution to the problem is that for every way of positioning the plane that allows for light to be diffused over space, a further point-source is required such that this is greater than zero-dimensional and involves therefore a finite quantity of concentrated light and a non-zero quantity of diffused light.

Note that nothing is to be done to the light, and thus that we have the idea of a universe which is created according to the ancient Hebraic tradition by the projection, not of light, but of space (the Genesis account of creation explicitly says that light came before any materiel source of light). This is a heuristic picture, but we can if we wish extract as much detail as we desire detail by identifying these differences with atoms: as the gap narrows, the atom concentrates light, jumps to a higher energy level; and as the gap widens, the atom diffuses light, jumps to a lower energy level… But what do atoms have to do with the prime numbers? By appeal to work on the primes conducted by Gauss and Riemann after Euler: Gauss speculated privately that the gaps between primes as we count down the number line grows logarithmically, and by appeal to Riemann’s 1859 paper *On the Number of Primes Less Than a Given Magnitude*, this was proved independently by Hadamard and de la Vallée Poussin in 1896. The object at the heart of the Riemann’s paper is called a “non-trivial zero of the zeta function” (symbolized by the lower case Greek letter Rho () and referring to the complex value of s such that the sum is equal to zero, and each of these zeros is associated with a different spiral-wave.

By combining these zero-based waves, a composite spiral-wave is produced.

This wave arises from the differences between the primes and the accurate simulating function

The Riemann Hypothesis says that the growth rate of this wave has a square-root amplitude, which is equivalential to saying that all the non-trivial zeros have real part equal to 1/2.

I propose that these atomic spiral-waves arise from the gaps there are between the artificial (pseudo-zero) origins and the natural (true-zero) origin in a way that is comparable to way that waves on the surface of a body water arise from disturbances -holes- in that surface. In other words, I propose that these spiral-waves arise from atoms, so that closing these gaps and disintegrating the atoms removes these holes and reduces the spiral to the zero-dimensional point which is/was their point of departure.

This proposal explains the “Montgomery-Odlyzko law”, which states that distribution of the spacing between successive nontrivial zeros of the Riemann zeta function (suitably normalized) is statistically identical with the distribution of eigenvalue spacings of the random matrices which are used to predict the energy levels of the nuclei of atoms.

It also explains the connection there is between number theory and quantum field theory. This connection can be simply illustrated by associating the creation operators and to the prime numbers … Now we have identified the unique ‘factorization’ of a state into creation operators acting on the ‘vacuum’ with the unique factorization of an integer into prime numbers (and we have a hierarchy of states: |1> is the ‘vacuum’; |2> and |3> and |5> are one-particle states; |6> is a two-particle state… and so on). By reference to the Witten index -the number of bosonic minus the number of fermionic zero-energy states- we see that the Mobius inversion function

*={1 = n has an even number of distinct factors,*

* -1 = n has an odd number of distinct factors, 0 = n has a repeated factor}*

is equivalent to the operator that distinguishes bosonic from fermionic states, with = 0 when n has a repeated factor being equivalent to the Pauli exclusion principle. If we re-express the Mertens function (which sums the 1s and -1s of the Mobius function) as , we see that sums of these states give us essentially the same composite spiral-wave as before.

Assuming that there are an equal number of non-zero-energy bosonic and fermionic states, this wave depicts the zero-energy fluctuations of these particles. Now we can go beyond the Montgomery-Odlyzko law and say that the Riemann Hypothesis is the governing principle of a physical theory according to which the superposition arising from these fluctuations possesses a square root growth rate. This is the same thing as saying that a) the non-trivial zeros of the zeta function have real part 1/2 and that b) these zeros are eigenvalues of the operations that on the one hand creates particles and on the other hand creates prime numbers. This wave protects us against the singularities of Relativity, and the infinities of Quantum Field Theory, and by flattening it, we are reducing the composite spiral to a point, but now this is, not merely a numerical but a physical operation: as this spiral-wave is flattened, the gaps between artificial point sources and the natural point source are being closed, and given that bosons can exist without any space between them, and fermions cannot, fermions are being annihilated by this operation. This is what the radiation/dematerialization hypothesis says happens to the body at the moment of resurrection, and it is what light-before-dark theory says happens if and when the universe is reverse-engineered. We have then the foundation of a new mathematical-physical theory in virtue of which the image on the Shroud was formed when the holographic projection that was the human body of the man in the Shroud was withdrawn by the disintegration of the atoms, and the closure of the gaps there are between non-zero dimensional origins the true-zero-dimensional origin, in virtue of which the body of the man in the Shroud existed in space and time and had a mass.

Narrowing the gap would cause the man’s body to take a brighter and less substantial form than a human body, as Jesus’ body is recorded as having done in Matthew 17:1 – 8, Mark 9: 2- 8, and Luke 9:28 – 36. Mathew 17: 2:

*There he was transfigured before them; his face shining as the sun, and his garments became white as **light.*

Closing the gap would cause the man to disappear and return to the zero-dimensional realm from which holographic projections arise.

This mathematics (of the Riemann Hypothesis) is essential to understanding this process for a variety of reasons, but most evidently because if the disintegration of the atoms in the body of the man on the Shroud went in the natural direction -the direction of the multiplication of primes to produce integers, and the direction in which prime-density is lost as we count down the number line- this would have resulted in a dramatic and rapid increase in volume during which great amounts of heat and light would be diffused. This is the space-creating/light-diffusing process familiar from Hiroshima and Nagasaki, and from Nuclear testing in the 50s and 60s. In this case, the tomb in the rock, and the whole of Jerusalem would have been destroyed. If however the disintegration went in the opposite direction -towards prime-density rather toward than prime-sparsity- then this is a light-concentrating/space-annihilating, process, and is to be accompanied by a decrease rather than an increase in volume. All things being equal, if the latter was the form of atomic disintegration undergone by the body in the Shroud, there would have been a small implosion rather than a large explosion at the moment of transformation. This second direction arises from a reversal of the effect produced by the artificial origins, and action of the mass gaps, and so if this was the form of disintegration undergone by the body in the Shroud, the image was impressed upon the fabric by reverse-engineering.

##### **part iii: the arrow of time**

**The Principle of Relativity**

In 1632 Galileo observed in the *Dialogue Concerning the Two Chief World Systems* that the laws of physics are the same in a ship traveling at constant velocity on a smooth sea as they are in a ship standing still:

*Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction… Have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.*

This observation has formed the basis of a principle known as ‘The Principle of Relativity’, which states simply that the laws of physics are the same for all observers in “inertial frames of reference”, i.e. observers at rest or moving uniformly in a straight line. Einstein discovered a contradiction involving this principle and the principle according to which light is propagated at the velocity c regardless of the motion of the emitting body. The figure below depicts a train, and a light source located in the center of a carriage, and an inconsistency between the perception of an observer inside and an observer outside the train.

From the point of view of an observer inside the train, light emitted from the center of the carriage reaches the front and the rear of the carriage simultaneously, but that from the point of view of an observer outside the train, the light reaches the front of the carriage first. It follows that at least one of the following principles is false:

- units of space and time are the same for all observers regardless of their states of motion
- the fundamental laws of physics are the same for all observers in inertial frames of reference
- light is propagated at the velocity c regardless of the state of motion of the emitting body

Given that 2 and 3 are true, it follows that 1 is false. It follows also that observers traveling at different velocities literally inhabit different spatio-temporal environments, different spaces and times. This is what leads to the famous twin-paradox, and all of the weirdness’s of Special Relativity. These paradoxes are due to the contraction of space and the slowing of time slows in the direction of the speed of light, and if per impossible one could travel at the speed of light, space and time would effectively vanish. In order to make sense of the concept of projection -and to avoid a circumstance in which there is an infinite concentration and a zero diffusion of light- it is necessary to work with artificial point sources. These are all tied to a solitary natural point source, from whose perspective light is infinitely concentrated. It follows that while it is possible to regard light as in motion against a background of space or vice versa in environments in which there is a balance of concentrated and diffused light (classical environments in keeping the Riemann Hypothesis), light is -absolutely speaking- at rest, and acquires the well-founded illusion of having a speed from the absolute motion of space. We must therefore revise the Theory of Relativity in terms of the principle that -absolutely speaking- it is light that is at rest, and it is space that expands equally in all directions at the minimum speed of c. The idea that light in a vacuum is propagated in straight lines at the velocity c is replaced by the idea that a vacuum expands in straight lines at the velocity c. Rather than

- light is propagated at the velocity c regardless of the state of motion of the emitting body

we have

- space expands at the velocity c regardless of the state of motion of the body in space

The curvilinear propagation of light in a gravitational field is replaced by the idea of the curvilinear propagation of space in a field of concentrated light. To apply this principle, take any situation in which we would be inclined to say that light is moving in respect of space and ask how space must be moving in respect of light to account for this impression. A symmetry arising from the balance of light and space, and prime density and sparsity, allows us to look at it in the former way (this is a well-founded illusion), but latter is what is really happening.

**The Expansion of the Universe**

The principles which emerged originally from the Special Theory of Relativity are these:

- the fundamental laws of physics are the same for all observers in inertial frames of reference
- light propagates at the velocity c regardless of the of the state of motion of the emitting body
- therefore units of space and time differ from observer to observer

From these principles we get the idea that units of space and time shrink in the direction of accelerated motion (equivalently, space and time shrink in the direction of the origin of a gravitational field, i.e. an artificial point source), so that as this motion approaches that of the speed of light (as the natural point source is approached), space and time tend to vanish. But since light is absolutely at rest, these principles are misleading, and the correct way to express them is this:

- the fundamental laws of physics are the same for all observers in inertial frames of reference
- space expands at the velocity c regardless of the state of motion of the body in space
- therefore units of space and time differ from observer to observer

But we know both from maths and from experiment that, while the expansion of mathematical and physical space may be regarded as locally uniform, this expansion is accelerating from a global point of view, and so we can revise 2 in this way:

- space expands locally at the velocity c regardless of the state of motion of the body in space, but there is a global expansion which is greater than c and which is accelerating

Richard Feynman in* The Character of Physical Law* invited us to imagine that atoms are divided into blue-coloured and white-coloured varieties, and separated into compartments. If the separation is removed, then just as blue dye turns water a luke-blue colour, the atoms form a luke-blue mixture. He observes that individual collisions provide no clue as to the irreversibility of the mixing process, but that studying a film of the mixing played in reverse reveals that

*…every one of the collisions is absolutely reversible, and yet the whole moving picture shows something absurd, which is that in the reverse picture the molecules start in the mixed condition… and as time goes on, through all the collisions, the blue separates from the white…*

He went on to say that

*…it is not natural that the accidents of life should be such that the blues will separate themselves from the whites…*

.The one-way nature of this process is reflected by from the experiment in which a gas is confined to one of two compartments. If the separation between the compartments is removed, then the gas spontaneously distributes itself in a uniform manner throughout the two compartments, but it does not spontaneously revert to the separated state. More familiar still, is the breaking of an egg. We never see a broken egg spontaneously reassemble, and there is no way to reassemble an egg after it has been broken (“All the kings horses and all the kings men couldn’t put Humpty together again.”). But although both these processes involve a one-way direction when viewed from a sufficiently global perspective, they can go either way when viewed from a sufficiently local perspective: the individual atoms comprising the gas molecules might just as well go from compartment B to compartment A as from compartment A to compartment B, and if we study the individual atoms comprising Humpty Dumpty we get no clue as to the fact that Humpty cannot be reassembled. Feynman’s answer that it is not natural is the sort of answer that can be legitimately given only when no deeper explanation is possible, when the thing standing in need of explanation is a self-explanatory or is a brute fact has been reached, and the irreversibility of classical phenomena is very far from being a brute fact. To explain it, we consider instead of blue and white coloured atoms that eventually form a luke-blue mixture, bosons (which can all pile up in a single zero-dimensional location) and fermions (and fermions that must be separated in space): in its fundamental light state, the universe involves no space, and no fermions, and the birth of the matter involves the introduction of space and fermions that produces a mixture of light and darkness. Again, the individual interactions between these particles provide no clue as to the irreversibility of the mixing process, but recalling the correspondence we earlier set up between the creation operators and to the prime numbers … and that the Mobius inversion function

*={1 = n has an even number of distinct factors,*

* -1 = n has an odd number of distinct factors, 0 = n has a repeated factor}*

is equivalent to the operator that distinguishes bosonic from fermionic states.

we can see exactly why this mixture of light and darkness appears balanced from a local perspective but why there is an irreversible trend toward the loss of light from a global perspective – reversing it and turning darkness back to light means contravening the Prime Number Theorem (no non trivial zeros with real part of 1) and the Riemann Hypothesis (no non-trivial zeros with real part other than 1/2).

To the naked eye the the distribution of the stars in the night sky seems to be random, but looking through a telescope we realize that galaxies have a spiral shape, light-dense toward the center of the galaxy, and increasingly dark at distance further away from the center. Same thing with the primes in the number line.

It is only by considering a sufficiently large group of stars and primes, and a sufficiently large group of particles, that the loss of energy-density known as ‘entropy’ is found to involve a one-way direction known as the arrow time. In fact there are multiple arrows of time. Well known are the thermodynamic arrow arising from the loss of heat, the cosmological arrow arising from the expansion of the universe, the radiative arrow arising from the expansion of waves outwards from their source, the causal arrow arising form the fact that effects follows causes rather than precede them, the quantum arrow arising from the collapse of the wave-function, and the psychological arrow of consciousness arising the fact that we remember the past and the future is unknown… Less well-known is the genetic arrow, which arises from the loss of mutability of DNA with generation, a consideration that explains anomalous results such as the apparent mismatch between Y-DNA extracted in 2014 from the skeleton of the English King Richard III and his contemporary paternal relatives, and points to the falsity of the Theory of Evolution (which depends on symmetrical DNA mutation rates). But the arrow that contains and explains all the others is the arithmetic arrow: if we play a film depicting the the un-breaking of an egg or the increase of the density of the prime numbers in the number line, we see something that looks absurd, and Feynman had no better explanation for this impression of absurdity in the first case other than ‘the accidents of life,’ But the impression of absurdity attached to the loss of density of the prime numbers as we count down the line isn’t an ‘accident’ at all – it is mathematically necessary that the repetition of a unit be accompanied by a global decrease in prime-density. The Riemann Hypothesis is an extension of the Prime Number Theorem: it says, not merely that the primes thin out, but that local changes in prime-density are equally likely to involve an increase as a decrease in density, and that they cannot exceed the upper and lower bounds marked in red and blue in the graphs below:

We can now extend the earlier principles:

- the fundamental laws of arithmetic are the same for all observers in inertial (arithmetically continuous) frames of reference
- there is a local balance of prime-density and prime sparsity which accounts for the apparent constancy of the speed of light, and allows for either light or space to be assumed to be a rest, there is a global loss of prime-density which accounts for the red-shifted nature of the light from distant stars
- therefore units of space and time and units number differ from observer to observer

We know from Euler’s thought-experiment that if prime-density were to increase sufficiently, there would be no units of number whatever, and what we would can say is that every observer has there own individual number line, each of which differs from that of every other observer. We can get at these different but interconnected number lines from Dirichlet’s observation that, so long as q and n have no common factor greater than 1, the progression q n + a involves infinite primes and that it is associated with an L-function (defined by the series ). All of these L-functions involve a local balance of prime-density and prime-sparsity (as dictated by the Generalized Riemann Hypothesis), and therefore fit the experimental data. But all involve different notions of unity and zero -different sets of primes and zeros because of different sets of artificial point sources- and a global and irreversible loss of prime-density. Correspondingly, energy-density is also dropping off in an irreversible manner, meaning that as the number line is turning irreversibly from number into space, the universe is turning irreversibly from light into darkness. “E = MC^2” now becomes “Energy = Mass times the expansion of space squared”, “M = E/C^2” becomes “Matter = Energy divided by the expansion of space squared.” But the two equations -one which describes the conversion of mass into energy and the other which describes the conversion of energy into mass- cannot as has been imagined be equivalent, because the expansion of space is, not constant, but is growing as a function of time (if C = 3 * 10^8 m/sec at time t1 and 3 * 10^9 m/sec at t2 then by multiplying M by 3 * 10^8 m/sec at t2 you obviously do not recapture E, and if the expansion of the universe is allowed to go on until a sufficiently late time tn, you will recapture only a small proportion of E).

By way of illustration, we can imagine Alice of Alice’s Adventures In Wonderland attempting to counter-act of expansive effects of a cake marked “Eat Me” by drinking potion from a bottle marked “Drink Me’ which results in contraction. Suppose that the cake caused her size to increase by halves so that first she was twice her original size, then a four times, then sixteen times, and so on…

It might seem that she can counter-act the expanding effect simply by taking a potion that iteratively halves her size until it returns to 1, but no. Alice can in some sense regain her original size in this way, but we know from the globally accelerated nature of the expansion of space that, regardless of any relative expansion or contraction, she and everything around her has undergone an absolute and dramatic to-scale expansion, and that this expansion is irreversible. From a global point of view, prime-density never increases with the repetition of an arithmetic unit, and equivalently, energy-density never increases with the repetition of a unit of space-time. And with this expansion and the accompanying loss of energy-density comes death. If Jackson’s hypothesis about the formation of the image on the Shroud is broadly the right one, then it was against this must fundamental of forces -the force that drives the universe from light into darkness, and everyman from life to death- that the man in the Shroud overcame.

**P versus NP and the Computational Arrow of Time**

There is a deep problem on the borderland of computer science, logic, maths and physics known as ‘P versus NP’, which concerns the question of whether the class of decision problems whose solutions are quickly verifiable (NP) by a computer is the same as the class of problems that are quickly solvable by computer (P). Historically the problem arose because certain problems seem to be hard to solve. More particularly, they seem to require a lot of time -an exponentially growing amount of time- to solve. An example of a NP problem that seeming takes exponential time is Factoring. While it doesn’t take long to factor 15 or 21, imagine trying to factor the 200 digit integer

27997833911221327870829467638722601621070446786955428537560009929326128400107609345671052955360856061822351910951365788637105954482006576775098580557613579098734950144178863178946295187237869221823983

You can easily check for yourself that it divides evenly into the primes

3532461934402770121272604978198464368671197400197625023649303468776121253679423200058547956528088349

and

7925869954478333033347085841480059687737975857364219960734330341455767872818152135381409304740185467

Although it takes a pocket calculator a spit second to do the multiplication, it would take a single 2.2 GHz computer roughly 75 years to do the division. Factoring is one is one of numerous (NP) problems that are easy in the one direction, and seem to be hard in the other. Here we have a further -computational- arrow of time. We can argue for the conclusion that this arrow really is asymmetric by considering the Travelling Salesman Problem, which is he problem of whether a salesman can visit a number of cities exactly once and return to a home-city for a certain cost.

First we transform it into a problem of whether a computer (salesman) can execute some number of instructions (visit some number of cities) which executes every instruction exactly once (visits every city exactly once) before returning to a halt state (home-city) for some maximum cost:

An arbitrary computer is therefore working on the problem of whether an arbitrary computer will halt when run with an arbitrary set of instructions, and thus the point will be reached when the evaluation is a self-evaluation, i.e. the point will be reached such that the computer is attempting to determine of itself if it will halt. If we associate to every city an instruction, this self-evaluative point will be reached when the number cities on the tour is the same as the number of instructions in the program. This leads to a contradiction in the case that the number cities is greater than the number of instructions, and by appeal to this contradiction, it follows that TSP involves a limit on the number of cities. This proves that TSP differs from polynomial-time problems, which aren’t aren’t sensitive to the size of the input, and that P and NP are not equal. More particularly… associate each atomic instruction in some finite set of instructions with some n-SAT formula (such as ), associate each of these formulas to the vertices of a complete graph other than the start/stop vertex. Associate the halt state with this start/stop vertex. Let v be the number of variables per clause, and if the instruction doesn’t result in the machine going into an infinite loop, weight the vertex as . If the instruction does result in the machine going into an infinite loop, weight the offending vertex as 0 + 1. Weight the halt vertex as 1. gives the minimum truth-density, , gives the maximum falsity-density of a satisfiable n-SAT instance, gives the maximum imbalance between the truth and falsity-density corresponding to a Travelling Salesman’s circuit that is within budget.

Let n be the number of instructions/vertices, and we can conclude that

- If and only if it is possible to visit every vertex exactly once before returning to a halt vertex for a cost n without upsetting the balance of minimum truth-density/maximum falsity density , there is some Turing machine that will not infinite loop when run with some input.

From here we get the equation and the idea that we can create any TSP circuit out of prime-circuits. Recalling the association of the creation operators and to the prime numbers … we can immediately associate these same operators to TSP circuits by reference to this equation. From the observations above, every TSP circuit, and every bosonic and fermionic state, can be assigned a place in a hierarchy of circuits/states based on the complexity of that circuit/state, and depending on where in that hierarchy that circuit/state appears, it can be determined whether or not some creation operator can complete some operation or whether or not some computer can complete some circuit under budget by appeal to the Mobius inversion function (it is possible to actually *count* the number of solutions to hard problems). By this line of argument, TSP problems can be identified with Factoring problems, and since the former are hard, so are the latter, as it is with the former, so it is with the latter. We can go one step further and identify the problem of computing the permanent of a square matrix (to compute the amplitude of n identical bosons to go from are an input to an output state we compute the permanent of a square matrix)

with Factoring. All of the differences between bosons and fermions arise from the difference between the computation of the permanent and the determinant

where the former is hard and the latter easy. A fast algorithm for Factoring, as a fast algorithm for the computation of the permanent, would collapse this hierarchy, and in 1994, Peter Shor introduced an algorithm which shows that quantum computers can factor integers in polynomial time, meaning that quantum computers can solve NP-Complete problems and compute the permanent of a square matrix, in polynomial time. Alan Turing conceived of an “oracle”, a computer able solve decision problems in a single operation. If it is possible for a program to run an input without any paying any computational time, the mathematical constraint on the computer which underpins the inequality of P and NP can be removed, and the program of such an all-powerful oracle is free to run inputs of any imaginable complexity. In a world without such a limit, P = NP, but the complexity of the inputs that can be run by real-world programs is limited because a program cannot in a finite period of time run an input whose complexity is equal to or greater than its own. In regard to these real-world limits, computer scientist Scott Aaronson has observed that the inequality of P and NP protects certain apparent physical laws. Suppose, he says, you set your computer working on an exponentially hard NP problem while you board a rocket ship that accelerates up to the speed of light and returns to earth only after the calculation has been completed. In space-time this might be an hour or so, but in earth time it might be millions of years. Trouble is that, while the time to make the computation has artificially become polynomial, the energy requirements of the rocket ship are exponential. Or suppose that you have a computer whose first operation is performed in 1 second, the next operation in 1/2 a second, the next in 1/4 of a second… and so on. Theoretically this computer has within 2 minutes performed an infinity of operations. Trouble is that the energy requirements of the cooling required to run a computer chip at this speed are exponentially great. Conversely, the equality and P and NP *unprotects* these laws… We can be more precise by arguing that the equality of P and NP implies that seemingly asymmetric direction of the loss of prime and energy-density governed by the Riemann Hypothesis is actually symmetric. In that case, a quantum computer has the ability to reverse the naturally irreversible, to reverse the direction of the arrow of time…. Isn’t this mathematically, and hence physically impossible, and so don’t we have a proof, not of the possibility of reversing the arrow of time, but of the impossibility of quantum computers? Not quite: the Riemann Hypothesis doesn’t say that prime-density and sparsity must involve the balance associated with the non-trivial zeros of real part 1/2, it says that in so far as a progression is arithmetically continuous it must involve this balance, i.e. it says that this balance is a necessary condition of arithmetic continuity). The impossibility proof there is here concerns “scalable” quantum computers, i.e. for quantum computers inhabiting the arithmetically continuous classical domain.

**Reversing the Arrow of Time**

Classically speaking, the solving NP-complete problems in polynomial time, and the reversal constituted by the resurrection, is impossible – skeptics are in a sense quite right to doubt that the dead ever come back to life on theoretical as well as empirical grounds. But it must always be remembered that the creation of the universe itself is an event that is classically impossible, a consideration that proves that non-classical events are in some sense necessary for the existence of classical events. We can therefore look upon the resurrection as a new creation. Otherwise put, we cannot place limits on what can come out of the natural point source that lies at root of the universe (where light is infinitely concentrated). The most that we can do -and I have attempted to show how this is to be done here- is to place limits on the *classical* things that can come out of this point source, but all the while knowing from the undeniable existence of this point source, and the undeniable fact of creation, that the non-classical is real, and that it is a precondition of the classical. Are these really undeniable? Do we really need any un-caused creative origin of our universe? Any denial will almost certainly proceed along the lines of Bertrand Russell’s denial in his 1948 debate with F. C. Copleston on BBC radio. During the course of this debate, Russell maintained over-and-against Copleston that “If anything can exist without a cause it may as well be the world as G-d”. If the world is a plurality (which it is), and G-d a singularity (which he is), then to say ‘If anything can exist without a cause it may as well be a plurality as a singularity’. But Russell -who knew little to nothing of quantum mechanics, the distinction between bosons and fermions, and the Pauli Exclusion principle, and nothing at all of the connection of physics to number theory – made a logical blunder, the logical blunder made every day by atheists: if G-d be pure light, then the claim that “If anything can exist without a cause it may as well be the world as G-d.” is equivalent to the claim that “If the number 1 can exist without the composites, then composites can exist without the number 1.” The number 1 *can* exist without the composites in the form of the singularity of concentrated light at root of Einstein’s universe, and at root of Euler’s extraction of all groups of primes and their powers from the harmonic series, but the converse is trivially false: otherwise put, matter is dependent on energy, but energy -whilst its presence is felt throughout the world- is independent of matter. Similarly, the world is dependent on G-d, but G-d -whilst his presence is felt throughout the world- is independent of that world (whilst the non-classical is present throughout the world, it is prior to the classical).

Normally, the human body exists in a state of relatively low and ever-diminishing energy-density. If the one-way direction of time were somehow turned back, and a body were to take on a sufficiently high state of energy-density, it would vanish. As early as 1989, physicist Thomas J. Phillips proposed that some of the features of the image on the Shroud, and the youthful radiocarbon date of 1988, could be explained by a thing called “thermal neutron flux”. According to this model, the sudden disintegration of the nuclei of the atoms in virtue of which the body of the man in the shroud possessed mass -which is akin to what would happen if the gaps between an artificial point sources and a natural point source governing the projection of the body in the Shroud were to close- would result a low-energy radiation signal such as could have both both created the image on the Shroud and skewed the radiocarbon date. Studies performed by Jean-Baptiste Rinaudo (1998) showed that a proton irradiated linen cloth is very similar in appearance to the body-image area on the Shroud:

And Robert A. Rucker (2014), a nuclear engineer and an expert in the calculation of neutron distributions in nuclear reactors, observed that if neutrons were released from the body in the Shroud, some if which would have been absorbed into N-14 in the Shroud to produce C-14, then this would cause the Shroud to be carbon-dated to younger than its true age. More particularly, if 2 * 10^18 neutrons were released form the body in the Shroud, this would increase the average C-14 content of the Shroud samples by 16%, which would suffice to shift the carbon date from 30AD to 1260 AD. The Raes sample was taken from a bottom corner of the Shroud, and Robert’s calculations imply that areas of the Shroud closer to the center of the body mass would contain more Carbon-14 and date, not to the middle ages, but as far into the future as 8500 AD. Since it takes a tiny proportion of the average number of neutrons in the average body (2 * 10^28) to skew the date, this means almost all of the energy in the body was retained rather than released, which agrees with the central idea of this note that the image was produced by a reverse-engineering mechanism obeying the mathematics described above. It disagrees profoundly with the idea that there was any nuclear disintegration going in a forwards direction. In 1988, the neutron flux hypothesis met with the response that this possibility had been considered by the laboratories participating in the carbon-dating of the Shroud, but dismissed because “No plausible physical mechanism has been proposed to explain how resurrection was accompanied by a significant neutron flux.”

Or as STURP member Alan Adler, has said of Jackson’s theory, it is not generally accepted as scientific because it runs counter to the laws of physics. But Adler is talking about the laws of physics accepted by him and his contemporaries, and these ‘laws’ arise in a context of a theory that is at best a low-energy approximation of the true theory. Jackson has preempted and diffused this objection by his thesis that the explanation of the image on the Shroud requires extension and revision of the accepted physical laws. This takes me to the conclusion to which I have been working throughout this note: the mathematical-physical framework outlined above, together with the oracular ability of a quantum computer running Shor’s algorithm, shows that a natural quantum computer is physical mechanism in full accordance with the laws of physics able to bring about the resurrection in a manner that accounts for image features of the Shroud.

Jackson and others have proposed that the body image on the Shroud was produced by the effect radiation on a cloth collapsing through a disappearing body, but there is something insufficient about cloth-collapse theories, and critics of the authenticity of the Shroud (such as David Kyle Johnson Ph. D who writes a* Psychology Today* blog called ironically *A Logical Take*) have mixed in with the usual pseudo-historical and pseudo-scientific objections some legitimate observations pertaining to this insufficiency:

*Just looking at the Shroud also establishes that it is not legitimate. First, the image in the shroud looks nothing like what Jesus would have actually looked like; first century Palestinians were not that tall (false, the vagaries of the cloth make it impossible to determine the exact height of man in the Shroud, but based on excavations in Galilee, this was not unnaturally far beyond the average for that time and place of 5’9), did not have that kind of hair or beard, or even that kind of nose. Instead, the image is more typical of how Jesus came to be depicted in art in the 14th century (false, the image is typical of how Jesus was depicted since the 6th or 7th century AD because these images were based on the image on the Shroud).*

*And speaking of the hair, the long hair seen in the shroud defies gravity. It is parallel with the man’s body, as if he is standing, instead of falling to the back of the head as it would if was the body were lying flat (true)…*

*Shroud enthusiasts-“shroudies,” as they like to be called- insist that the image on the shroud was produced by some kind of energy (like radiation) emitted by Jesus’s body as he rose. But the image on the shroud could not be produced by such an event. (A) Radiation can’t leave an image in cloth (false). (B) Even if it could, since radiation emits in all directions, at best it would just leave a blurry silhouette, not a clear cut face with features (false, high frequency radiation produces a clear image). (C) Even if it could produce a clear cut face with features, that face would be distorted. A cloth wrapped around someone’s head lays flat against their nose, eye sockets and ears. If someone’s face somehow ‘radiated’ and recorded an image on such a cloth, when flattened out the cloth would depict whole representations of each part – nose, eye socket, and ears – all pointing in the same direction (true, assuming the presence of gravity)…*

Cloth-collapse models simply can’t account for phenomena -such as the lack of any side image, and the undistorted nature of the frontal and dorsal images- suggestive of an absence of gravity, but the late artist Isobel Piczek provided the hint of a theory that can. She noted:

- The lack of anatomical distortion of the naked Body projected on the Shroud.
- It is clearly visible on the Shroud Images, especially on the Dorsal Image, that the muscles of the Body are not crushed and flattened against the stone bench of the tomb.
- The Body is hovering between the upper and the lower sheet and there is NO TRACE OF GRAVITY.
- The lack of gravity is also further proven by the Shroud linen. The linen does not fall on top of the Body, but remains in its unnaturally stretched condition at some distance from the body.

And while her theory doesn’t make make sense in terms of the space-centric Theory of Relativity that has come down to us from Einstein, it does make sense in terms of the energy-centric theory outlined above according to which the initial condition of the universe is pure energy, that light therefore has zero speed, and so that the expansion of the universe against this background of light is the basis of the apparent speed of light, and of the tension between the dark energy that increasingly pulls the universe apart and the ‘light energy’ that holds it together: gravity is on this account, not a true force, but an epiphenomenon of the action of the force causing the acceleration of the expansion of the universe, and so the suspension of this expansion required to raise body in the Shroud from the dead would indeed be accompanied by the seeming suspension of gravity. That this suspension is possible for a quantum computer is not to say that any man-made mechanism or any mechanism of terrestrial origin can do such things, for all such mechanisms inhabit the classical domain, and are thus limited by the problem known as ‘quantum decoherence’, i.e. the collapse of a quantum superposition (the wave-function) by the interaction of the quantum computer/system with its environment. The central experiment of quantum mechanics – the experiment from which all quantum weirdness arises- involves the shooting of particles through 2 narrow slits and measuring their arrival on a screen behind the slits. If detectors are attached to the slits, a pair of Gaussians appears on the screen, one between each slits, but otherwise an interference pattern such as would be produced by a wave appears. This leads to the thought that a superposition of waves known as a ‘wave-function’ describes the particle as it is independently of measurement, a superposition that implies that the particle traveled through both slits at once and interfered with itself. This leads to the paradox of Schrodinger’s Cat, a thought-experiment concerning a cat is imprisoned in chamber into which a poisonous gas will be released dependent on the behavior of a quantum system: the 2-slit experiment has seemed to some to imply that the cat is in a joint state of alive + dead until the system is measured.

The great flaw in all of the conventional interpretations of the 2-slit experiment -most especially the ‘many worlds’ interpretation which would have us believe that the universe breaks into independent branches whenever a quantum system is measured- is the failure to appreciate that classical systems are themselves superpositions – they are the long-ranged symmetric superposition that arise from the waves associated to the non-trivial zeros of L-functions that we have considered above. Schrodinger’s cat is such a classical system, and is thus at all times either alive or dead, and not both, regardless of what the quantum system in the thought-experiment does. But this is not true of a quantum systems, which are the short-ranged asymmetric superposition associated to the sources of these long-ranged superpositions. According to these conventional interpretations of quantum mechanics, the act of measurement -such as the act a of measuring device attached to the slits- collapses the superposition, but this is the wrong way to look at it. Another way to characterize the essence of this kind of interpretation is to say that, according to such interpretations, the presence of the 2-path information of arithmetic consciousness collapses the superposition, and this is the reverse of the truth. Rather, it is the collapse of a the quantum superposition that produces the 2-path information of arithmetic consciousness. This follows from the nature of the connection between number theory and quantum field theory and complexity theory outlined above: given the association of the creation operators and to the prime numbers … we can associate these same operators to Travelling Salesman circuits circuits by reference to the equation

Every TSP circuit can we know be assigned a place in a hierarchy of circuits such that there is a point at which the complexity of a computational problem is as great as the complexity of the means of solution, a point that marks a collapse, the end of one program and the beginning of another. Assuming that there are an equal number of non-zero-energy bosonic and fermionic states, the imbalance in the sum

concerns the zero states, which are the mass gaps in virtue of which light is diffused. These correspond to the differences between TSP inputs and programs, and the point at which these are in balance, which is the point at which there is a balance of concentration and diffusion represented by the intersections of the x-axis by the wave below is a limit that marks a collapse, the end of one mass gap and the beginning of another:

These limits coincide with the prime numbers and the atomic classical superpositions that form the basis of all arithmetic progressions, and with the zeros of L-functions and the atomic quantum superpositions that form the basis of the primes and classical superpositions. The meaning of the 2-slit experiment is this: the light/dark symmetric classical universe is a projection arising from light-dominant asymmetric non-classical projective sources. There is then no sense in trying build scalable quantum computers, i.e. quantum computers that inhabit the classical domain. A billion dollar industry has grown up built around the quest to build these machines (and toy quantum computers that can factor very small numbers no faster than a pocket calculator have already been built, and toy quantum computers are the only quantum computers that will ever be built), but the quest is based on a misconception of the relationship between the classical and the quantum domains. This misconception is that quantum systems are the building blocks of classical systems in the same sense in which bricks are the building blocks of brick walls, which implies that a classical system (a brick wall) is merely a scaled up version of quantum systems (bricks). This is a more or less unanimously accepted picture of the universe, but a false one – if you follow a classical system back in time as far as possible, you will not come to a pile of very little quantum brick, but to a maximally energy-dense classical system that appeared at the moment of creation in an instant. The true picture can be formed by using the projection/projector metaphor. In the light of this metaphor, physics since the time of ancient Greek atomists has been based on an category mistake that equivocates between the projection (classical) and the projector (non-classical): projected (classical) domains possess a particular balance of concentrated light and diffused light governed by the Riemann Hypothesis, whereas the domains of the projectors (non-classical) possesses an imbalance in favour of concentrated light. More particularly, the projectors (the artificial point sources of which we spoke earlier) produce Riemann Hypothesis-friendly balances of light and space in the form of projections – more precisely, they produce spiral-waves associated to the non-trivial zeros of L-functions- but are themselves light-dominant. But every projection is finite. When the projector and the projection approach the balance at which they are the same -the balance at which at which the gap between the projector and the projection becomes very small- the projector loses the properties that made it computationally powerful in its quantum state (the wave-function of the projector as they say collapses). Like all the arrows of time, the quantum arrow is a form of the arithmetic arrow, the action of a natural quantum computer is able to reverse the destructive direction of this arrow, but this not the action of a classical device or object, but of something that transcends the classical domain.

The bible is full of accounts of events that involve such reversals: the parting of the red sea to allow the children of Israel to escape from Egypt, the collapse of the walls of Jericho, the ascent into heaven by the prophet Elijah, and so on and so on. But -along with the creation itself- the greatest of these stories by far is that of the resurrection of Jesus -Yeshua ben Yosef- who identified himself as the Jewish Messiah and the son of G-d, and from all accounts rose from the dead by his own power. According to the bible, Yeshua was, like you and I, in the sense that he was a part of the classical universe, and he bled, suffered terribly, and died. But it says also that he rose form the dead within three to four days, and so that these experiences were for him unnecessary: that he had it within his power to overcome death itself, shows that he had it within his power not to bled, suffer, and die. His story is that of someone who had it within his power to defeat the dark energy, and to reverse the arrow of time and the reason that all of kings horses and all the kings men could not put Humpty Dumpty together again. Less poetically, he had it within his power to cross to the high-energy side of the divide signified by the balance of prime and energy-density given by the Riemann Hypothesis as a condition of arithmetic consciousness. This is the ability possessed someone whose origin is in the realm beyond the smallest mass gap -a realm outside of our classical universe- and it is an ability that accounts for his virgin birth, his miraculous powers (powers unparalleled by any other biblical figure or by any figure in human history), the transfiguration, the resurrection, and for the ascension. It is also accounts for the mysterious image upon the cloth we call the Shroud of Turin (and arguably also for the incorrect carbon-dating of the cloth).

##### APPENDIX A: SUMMARY OF STURP’S CONCLUSIONS

The Shroud of Turin is a 14.3 foot by 3.7 linen cloth bearing the faint double-No pigments, paints, dyes or stains have been found on the fibrils. X-ray, fluorescence and microchemistry on the fibrils preclude the possibility of paint being used as a method for creating the image. Ultra Violet and infrared evaluation confirm these studies. Computer image enhancement and analysis by a device known as a VP-8 image analyzer show that the image has unique, three-dimensional information encoded in it. Microchemical evaluation has indicated no evidence of any spices, oils, or any biochemicals known to be produced by the body in life or in death. It is clear that there has been a direct contact of the Shroud with a body, which explains certain features such as scourge marks, as well as the blood. However, while this type of contact might explain some of the features of the torso, it is totally incapable of explaining the image of the face with the high resolution that has been amply demonstrated by photography.

The basic problem from a scientific point of view is that some explanations which might be tenable from a chemical point of view, are precluded by physics. Contrariwise, certain physical explanations which may be attractive are completely precluded by the chemistry. For an adequate explanation for the image of the Shroud, one must have an explanation which is scientifically sound, from a physical, chemical, biological and medical viewpoint. At the present, this type of solution does not appear to be obtainable by the best efforts of the members of the Shroud Team. Furthermore, experiments in physics and chemistry with old linen have failed to reproduce adequately the phenomenon presented by the Shroud of Turin. The scientific consensus is that the image was produced by something which resulted in oxidation, dehydration and conjugation of the polysaccharide structure of the microfibrils of the linen itself. Such changes can be duplicated in the laboratory by certain chemical and physical processes. A similar type of change in linen can be obtained by sulphuric acid or heat. However, there are no chemical or physical methods known which can account for the totality of the image, nor can any combination of physical, chemical, biological or medical circumstances explain the image adequately.

Thus, the answer to the question of how the image was produced or what produced the image remains, now, as it has in the past, a mystery.

We can conclude for now that the Shroud image is that of a real human form of a scourged, crucified man. It is not the product of an artist. The blood stains are composed of hemoglobin and also give a positive test for serum albumin. The image is an ongoing mystery and until further chemical studies are made, perhaps by this group of scientists, or perhaps by some scientists in the future, the problem remains unsolved.

##### APPENDIX B: THE ALLEGED CONFLICT BETWEEN THE SHROUD AND THE GOSPELS

The Synoptic Gospels (Mathew, Mark, Luke) all confirm that Jesus was wrapped in a linen cloth, a ‘sindon’:

*Mathew 27: 59 Joseph took the body, wrapped it in a clean linen cloth.*

*Mark 15:46 So Joseph bought some linen cloth, took down the body, wrapped it in the linen, and placed it in a tomb cut out of rock. Then he rolled a stone against the entrance of the tomb.*

*Luke 23:53 Then he took it down, wrapped it in linen cloth and placed it in a tomb cut in the rock, one in which no one had yet been laid.*

The meaning of ‘sindon’ is

*linen cloth, esp. that which was fine and costly, in which the bodies of the dead were wrapped*

The word is used in the singular: Mark describes the piece of material in which Jesus’ body was wrapped as a ‘sindon’ (Mark 15:46) and he describes the garment worn by the young man who fled naked on the night of Jesus’s arrest as a ‘sindon’ (Mark 15:51). The Shroud of Turin is a sindon, a fine linen cloth, whose 3 over 1 herringbone weave is particularly elegant and rare.

The gospel of John however seems to contradict the synoptic gospels, saying

*John 19:40 Taking Jesus’ body, the two of them wrapped it, with the spices, in strips of linen. This was in accordance with Jewish burial customs.*

And later

*John 20: 5-7 He bent over and looked in at the strips of linen lying there but did not go in. Then Simon Peter came along behind him and went straight into the tomb. He saw the strips of linen lying there, as well as the cloth that had been wrapped around Jesus’ head. The cloth was still lying in its place, separate from the linen.*

But the word from which the English expression ‘strips of linen’ supposedly translates is ‘othonia’, when the latter actually refers to cloth of all sizes and shapes. The Greek writer Dioskorides not only used ‘orthonia’ to mean a sheet but coupled it with the verb ‘enelein’, which is the verb Mark used to describe the wrapping of Jesus’ body in linen (‘eneilisenti sindoni’). Evidence that John did not intend the meaning ‘strips of linen’ comes from a passage in Luke (Luke 24:12) where Luke describes what he has previously described in Luke 23:53 as a ‘sindon’ (a single cloth) as ‘orthonia’:

*Luke 23: 53 Then he took it down, wrapped it in linen cloth and placed it in a tomb cut in the rock, one in which no one had yet been laid.*

*Luke 24:12 Peter, however, got up and ran to the tomb. Bending over, he saw the strips of linen lying by themselves, and he went away, wondering to himself what had happened.*

John also says that Jesus was buried according to Jewish burial customs, and unlike the Egyptians, the Jews did not mummify their dead. Lazarus was bound hand and foot -and it is more than likely that Jesus too was bound into the Shroud- but the word used by John to describe this is, not ‘othonia’, but ‘keiriai’. It is clear that John has been mistranslated, and that what he and Simon Peter saw lying in the tomb were, not primarily “strips of linen”, but the single fine linen cloth or ‘sindon’ that according to the synoptic gospels was used by Joseph of Arimathea to wrap the body of Jesus after the crucifixion. Separate from this was the cloth that had been wrapped around Jesus’ head. It is arguable that both of these cloths have survived to this day, the first as the Shroud of Turin, and the second as the Sudarium of Oviedo.

##### APPENDIX C: SHROUD-DENIAL

**The Mystery of the Shroud**

The central mystery of the Shroud of Turin is, and always has been, how the image was imposed upon the cloth. Numerous attempts have been made to duplicate it, and all have failed. It may very well be true, as historian Antonio Lombatti maintains, that the Shroud was one of 40 supposed burial cloths of Jesus in circulation during the middle ages, but so what? That there are 40 forgeries of Vermeer’s *Girl With a Pearl Earring* in circulation does nothing to cast doubt on the existence of an original painting… Moreover, if all our considerable efforts and ingenuity -the Shroud is by far the most analyzed artifact in history- have proven insufficient to unambiguously expose a fake made using primitive technology, then either our analytical methods are unreliable or the Shroud is genuine. And not only have we been unable to unambiguously expose the Shroud as a fake, the consensus amongst those scholars who conducted the longest and deepest investigations into this matter is that it is genuine. In the words of the Shroud of Turin Research Project (STURP):

*We can conclude for now that the Shroud image is that of a real human form of a scourged, crucified man. It is not the product of an artist .*

The authenticity of the Shroud, it can be argued, is a condition of the reliability of our present scientific methods for understanding the universe.

**The Psychology of Shroud-Denial versus Shroud-Affirmation**

There is -it can not be reasonably denied- a considerable weight of evidence in favor of the authenticity of the Shroud: scientific theories have gained world-wide acceptance on a basis of less evidence; people -not least of all Jesus himself- have been sentenced to death on the basis of less evidence (believers in the authenticity of the Shroud are often called ‘the faithful’ as if they believe in spite of the great amount of evidence revealing it to be a fake, but it might be objected that in the light of the amount of evidence for the authenticity of the Shroud it is the disbelievers in the authenticity of the Shroud that are ‘the faithful’). The barrier to belief is, not the weight of evidence to the contrary -there is really one a single contrary and easily disposable contra-indication- but the implications of the Shroud for the nature of the universe and man’s role in in it. These are so unwanted at the psychological level that many apply to it higher standards of proof than would normally be applied, and seize upon every possible sign that it is a fake. But surely, it might we objected, the pro-Shroud brigade are no less liable to bias than are the con-Shroud brigade; surely they apply *lower* standards of proof than would normally be applied, and seize upon every possible sign that it as *genuine* (Shroud-deniers often argue for example that the STURP team were biased, but in fact many were initially agnostic or skeptical). There is an important difference. Non-Christian Shroud-deniers are more likely to be negatively biased because the authenticity of the Shroud coheres with and therefore is evidence in favor of the central element of Christianity (Jesus’ death and resurrection), whereas for a Christian its in-authenticity is irrelevant. Elaborating, if one disbelieves the central tenet of Christianity, then one expects that there is nothing extraordinary about Jesus’ burial Shroud, and if a claimed burial Shroud exists that does posses extraordinary properties, then one expects that it is inauthentic. If by contrast one believes the central tenet of Christianity, then one need have no expectations regarding the nature of Jesus’ burial Shroud whatever. Certainly, a Christians’s belief structure is not in the least impacted by the existence of a fake Shroud. Perhaps the paradigmatically dispassionate attitude to the Shroud belongs to Barrie Schwortz. An orthodox Jew, and a reluctant and skeptical member of the original STURP team who took 17 years to accept that the Shroud was authentic, Barrie’s later role as the world’s foremost proponent of the Shroud’s authenticity is based solely on the strength of the historical and scientific evidence.

A number of philosophers, including Wittgenstein, Kuhn, and Quine, have written of a mechanism that helps explain the bias of the Shroud-deniers. These philosophers point out that our belief systems may understood as possessing a loosely hierarchical structure, a structure such that beliefs are arranged according to their logical priority, according to their depth. And they point out that deep-rooted beliefs are not readily abandoned or revised. Let me give an example concerning the belief in the classical understanding gravity. Belief in the classical law of gravity is deeper than any belief about the behaviour of a dropped-cup. If such a cup seemed to float to the ceiling rather than fall to the floor, then maybe it was dropped by someone in a spaceship or in some gravity-diminished environment, or maybe it was a cup-shaped helium balloon… Better these explanations than a revision of the classical law of gravity because when we are confronted with a relatively shallow piece of evidence that apparently conflicts with a deep-rooted belief we will -presumably for reasons of epistemic economy- tend to try and find a way to discount the shallow evidence. Speaking of revising the law of gravity, one of the buzz-topics in physics has been ‘dark matter’. The flat rotation curves of galaxies can be regarded as shallow pieces of evidence that conflict with the deep-rooted belief that the law of gravity as it appears in Newtonian physics and in General Relativity is correct. Similarly, the Shroud can be regarded as a shallow piece of evidence that conflicts with the deep-rooted belief of many that the biblical account of Jesus’ death is false. Such is their commitment to classical physics, that many physicists would rather believe in the presence of a pervasive, but invisible and undetected substance than accept that the universe is governed by a different set of laws than those proposed by Newton and Einstein. And such is their commitment to an anti-Christian world-view that many skeptics would rather entertain the idea that the image on the Shroud was forged by Leonardo Da Vinci (who was born in 1452, 97 years after the first public presentation of the Shroud in 1335) than accept its authenticity. As indicated above, no such conflict exists for the Christian: he or she may find the idea that the Shroud is authentic to be appealing, but there is no tenet of Christianity that implies or even suggests its authenticity, and so no conflict arises from the possibility that it is a fake. Indeed many of the Shroud’s most ardent critics are Christians. John Calvin for example asked in his *Treatise on Relics*

*How is it possible that those sacred historians, who carefully related all the miracles that took place at Christ’s death, should have omitted to mention one so remarkable as the likeness of the body of our Lord remaining on its wrapping sheet?”*

For one thing, there is a Jewish taboo corcerning the removal of grave-clothes from a tomb, for another, Jesus’ disciples were -as members of what was then a heretical sect- in a vulnerable position following his death, but perhaps the simplest answer to Calvin’s query is that the image is a very faint negative that can only be seen from several meters away, the majority of whose features only became discernible 20 centuries later – portentously, the Shroud is a message -“I am alive.”- that can be properly understood only by those living in the 20th and 21st centuries. Non-Christians are motivated to deny the authenticity of the Shroud in a way that Christians are not motivated to affirm it: if a non-Christian can’t deny the authenticity of the Shroud, then they must face the prospect that the gospels offer a true account of the life of Jesus, and this prospect is at very least a disquieting one, since it implies that they will be held accountable for their lives. In particular, atheists will believe anything rather than believe in the resurrection. Their commitment to a world without resurrection runs so deep that they will concoct any story no matter how implausible. The most implausible -and the funniest- of these atheistic narratives I know of comes from another historian, Thomas de Wesselow, who in 2012 published a book claiming that a) the image on the Shroud is an image of Jesus of Nazareth following his death by crucifixion formed by natural chemical processes, but more significantly that b) it was later used to fool the disciples into believing that Jesus had risen from the dead (behold this negative, barely discernible discolouration in the shape of man, for it is the risen Christ):

Many physicists may be predisposed to a belief in dark matter for the innocent reason that they can’t think of any better theory than General Relativity. One of the pioneers of the discovery of the flat rotation curves -Vera Rubin- inclines to the idea that dark matter is a sign that the traditional 1/r^2 force law is modified at galactic scales:

*If I could have my pick, I would like to learn that Newton’s laws must be modified in order to correctly describe gravitational interactions at large distances. That’s more appealing than a universe filled with a new kind of sub-nuclear particle.*

There are strong indications however that Shroud-deniers have dismissed the alternative for psychological reasons. Consider some typical responses to a newspaper article describing the work of a team headed by Dr Paolo Di Lazzaro who after a their series of tests decided that the image on the Shroud could only have been created by “some form of electromagnetic energy” such as a flash of light at short wavelength but that the energy required was too great for contemporary technology. I choose to quote the following comments because of the article’s unjustified use of the word ‘supernatural’ (Di Lazzaro’s team did not say that the image on the Shroud was produced by supernatural means, only that the probable means of production were such that it could not have been the work of a medieval forger):

*“Has this work been peer-reviewed? Where is it published?”*

*“And they call these people scientists in Italy, do they? How quaint.”*

*“Galileo must be turning in his grave. I suspect the inquisition got to em.”*

*“Scientists ? hahahahahahaha*

*Since the Shroud has been radiocarbon dated independently by labs in Arizona, Oxford and Zurich with the result that the Shroud was made between 1260 and 1390 one has to assume that their theory is a tiny bit wrong …..*

*Or perhaps the fact that radiocarbon dating shows the Shroud to be a fake is another miracle ? Perhaps these “scientists” believe that God was not only using UV lasers but also removed C-14 isotopes from the Shroud ?”*

*“Sorry, This is junk science. Amazing they published. It is the total dose (intensity X time), not a one off ‘flash’.*

*Further, this rag was carbon dated to well after the time of the supposed death of the mythological son of an mythical construct, based upon Assyrian myths from 4500 years ago.*

*Probably a timely piece to encourage the decreasing numbers of ‘believers’..”*

*“I just spat out my morning corn flakes reading this tripe!*

*The corn flakes then formed a perfect image of Virgin and Child on my kitchen table.*

*It must be true – I’m off to church.”*

*“Meh! What is it with those nutbars? As the irrationality and absurdity of religion becomes increasingly obvious, they try to harness a tailored version of science to impress people. If their sky fairy really existed and wanted to give us a message, I’m sure it would have done so much more directly a long time ago.”*

*“Another story about more Jesus botherers and their pathetic ‘evidence’ of something that could be mistaken for being an unsupernatural event……and this indeed was another of those events. I’m sorry, but if you think Jesus was some real supernatural son of some creator of this universe, and that this creator used his magic powers to do this Shroud, then you are simply stupid.*

*Why should even the slightest bit of respect be given for any simpleton who believes this nonsense?”*

The wording on these comments is suggestive, not of dispassionate contemplation, but of hatred and its parent emotion fear, emotions that are directed especially toward the idea of a world governed by quite different principles than the ones that the authors have naively accepted as the true ones.

##### REFERENCES

Antonacci, M (2001), Resurrection of the Shroud: New Scientific, Medical, and Archeological Evidence

http://www.scottaaronson.com/blog/

Benford, M, and Marino, J (2002), Textile Evidence Supports Skewed Radiocarbon Date of Shroud of Turin

Brooks, M (2005), 13 Things That Don’t Make Sense

Calvin, J (1543), Treatise on Relics

Carreria, M (2010), The Shroud of Turin From the Viewpoint of the Physical Sciences

Carroll, L (1865), Alice’s Adventures in Wonderland

http://www.claymath.org/millennium-problems/yang%E2%80%93mills-and-mass-gap

Cook, S (1971), The complexity of theorem proving procedures

Danin, A, et al (1999), Flora of the Shroud of Turin

Damon, P, et al (1989), Radiocarbon dating of the Shroud of Turin

de Malijay, A (1930), La Santa Sindone di Torino

de la Vallée Poussin, C (1896), Recherches analytiques la théorie des nombres premiers (Analytical research on the theory of prime numbers)

de Swart, J. et al (2017), How dark matter came to matter

de Wesselow, T (2012), The Sign: The Shroud of Turin and the Birth of Christianity

Di Lazzaro, P (2011), Shroud\[Dash]Like Coloration of Linen Fabrics By Vacuum Ultraviolet Radiation

Dirichlet, P (1837), Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält” (Proof of the theorem that every unbounded arithmetic progression, whose first term and common difference are integers without common factors, contains infinitely many prime numbers)

Einstein A. (1916), Relativity: The Special and General Theory

Euler, L (1737), Variae observations circa series infinitas (Various observations concerning infinite series)

Fanti, G (2011) Hypotheses regarding the Formation of the Body Image: A Critical Compendium

Felis, F (1982), The Dating of the Shroud of Turin from coins of Pontius Pilate

Ferri, L (1986), Volto senza tempo (Face Out of Time)

Feynman, R (1964) The Character of Physical Law

Galileo, G (1632), Dialogue Concerning the Two Chief World Systems

Hadamard, J (1896), Sur la distribution des zéros de la fonction zeta(s) et ses conséquences arithmétiques (On the distribution of the zeros of the zeta function and some consequences for arithmetic)

Havil, J (2003), Gamma: Exploring Euler’s Constant

Johnson, D (2014), Let Go of the Shroud: It’s obviously fake

Jones, A (2016), Five Great Problems in Theoretical Physics

King, T, et al (2014), Identification of the remains of King Richard III

Kohlbeck, J, and Nitowski, E (1986), New evidence may explain image on Shroud of Turin

Kuhn, T (1962), The Structure of Scientific Revolutions

Lombatti, A (2000), Sfida alla Sindone (Challenge the Shroud)

Jackson, J (1990) Is the image on the Shroud due to a process heretofore unknown to modern science?

Jackson, J (1991), An unconventional hypothesis to explain all image characteristics found on the Shroud image

Juskalian, R (2017), Practical Quantum Computers: Advances at Google, Intel, and several research groups indicate that computers with previously unimaginable power are finally within reach

Little, K (1997), The formation of the Shroud’s body image

Martin-Lopez, E, et al (2012), Experimental realization of Shor’s quantum factoring algorithm using qubit recycling

http://mathworld.wolfram.com/

Maxwell, James Clerk (1865), A dynamical theory of the electromagnetic field

Meyers, E, et al (1981), Excavations at Ancient Meiron, Upper Galilee, Israel

Milgrom, Mordehai, (1983), A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis

Montgomery, H (1973), The pair correlation of zeros of the zeta function

Newton, I (1687), The Principia: Mathematical Principles of Natural Philosophy

Odlyzko, A (1987), On the distribution of spacings between zeros of the zeta function

Newton, I (1687), The Principia: Mathematical Principles of Natural Philosophy

http://www.newtonproject.ox.ac.uk/view/texts/normalized/THEM00258

Peebles, P, and Ratra, B (2003), The cosmological constant and dark energy

Phillips, T (1989), Shroud irradiated with neutrons?

Picknett, L, and Price, C (2007), The Turin Shroud: How Da Vinci Fooled History

Plato, Theaetetus

Piczek, I, The Event Horizon of the Shroud of Turin

Quine, W (1951), Two Dogmas of Empiricism

Riemann, G (1859), Über die Anzahl der Primzahlen unter einer gegebenen Grösse (On the Number of Primes Less Than a Given Magnitude)

Rinaudo, J (1999), Image formation on the Shroud of Turin explained by a protonic model affecting radiocarbon dating

Rogers, R (2005), Studies on the radiocarbon sample from the shroud of turin

Rubin, V, et al (1980), Rotational Properties of 21 Sc Galaxies with a Large Range of Luminosities and Radii from NGC 4605 (R = 4kpc) to UGC 2885 (R = 122kpc)

Rucker, R (2014), MCNP Analysis of Neutrons Released from Jesus Body in the Resurrection

Ruffin, B (1999), The Shroud of Turin

Russell, B, and Copleston, F (1948), The Existence of God, in John Hick, ed., The Existence of God

Shor, P (1995), Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Schwortz, B (1996), http://www.shroud.com/

Spector, D (1990), Supersymmetry and the M\[Delta]bius Inversion Function

Smolin, L (2006) The Trouble with Physics:The Rise of String Theory, the Fall of a Science, and What Comes Next

A Summary of STURP’s Conclusions (1981)

Taylor, C (1999), The atomists, Leucippus and Democritus: Fragments

Turing, A (1937), On Computable Numbers, with an Application to the Entscheidungsproblem

Turing, A (1939), Systems of Logic Based on Ordinals

Vignon, D (1902), The Shroud of Christ

Whanger, A (1994), A comparison of the Sudarium of Oviedo and the Shroud of Turin using the polarized image overlay technique

Whanger, A (2000), Evidence for Radiation from the Shroud Image Itself in the Formation of the Shroud Images

Whiting, B (2006), The Shroud Story

Wilson, I (1998), The Blood and the Shroud

Witten, E (1982), Constraints on supersymmetry breaking

Xu, N, et al (2012), Quantum Factorization of 143 on a Dipolar-Coupling Nuclear Magnetic Resonance System